Download Bone Conduction Transducers and Output Variability

Bone Conduction Transducers and Output
Variability
Lumped-parameter modelling of state variables
Master of Science Thesis in Biomedical Engineering
HERMAN LUNDGREN
Department of Signals and Systems
Biomedical Signals and Systems Division
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden, 2010
Report No. EX0042/2010
Title: Bone Conduction Transducers and Output Variability
Subtitle: Lumped-parameter modelling of state variables
Report No. EX042/2010
Chalmers Institute of Technology
Göteborg, Sweden, 2010
Department of Signals and Systems
Biomedical Signals and Systems
Abstract
Bone-conduction transducers for hearing aids are used by thousands of patients that cannot use conventional air-conduction hearing devices. Such
bone conduction transducers have also been extensively used in bone conduction audiometry, for example, hearing threshold measurements. The interaction between these transducers output impedance and the patients skin
impedance over the temporal bone, which both are in the same range, results in a high variability of the output force, acceleration and power which
is directly related to the variability in the patients skin impedances. Because
the output force is used as the reference zero standard for bone conduction
hearing thresholds, variability in patient skin impedances is a source of error
in threshold determination via bone conduction. This work investigates the
extent of this variability in the output from one Radioear B71 transducer
due to the skin impedances of 30 subjects. In the frequency range 100-10000
Hz, an inter subject standard deviation in the skin impedance, averaging
2.4 dB, gives rise to a standard deviation in force and acceleration output
ranging from 0 - 5 dB. The impedance characteristic of the transducer can
be used to predict which frequency regions correspond to increased output
variability, as well as to nd "golden" frequency areas having less force and
acceleration output variability.
Contents
1 Introduction
1
2 Background/Theory
3
2.1
Biology and Mechanics of Hearing
. . . . . . . . . . . . . . .
3
2.2
Hearing Loss
. . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.3
Audiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.3.1
Calibration for BC Audiometry . . . . . . . . . . . . .
7
2.3.2
Sources of Error
9
. . . . . . . . . . . . . . . . . . . . .
2.4
Bone Conduction Hearing Devices
2.5
Modelling and Simulation
2.4.1
. . . . . . . . . . . . . . .
The B71 . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
9
10
10
2.5.1
Electrical/Mechanical Analogies . . . . . . . . . . . . .
11
2.5.2
Two-Port Models . . . . . . . . . . . . . . . . . . . . .
12
2.5.3
Lumped Parameter . . . . . . . . . . . . . . . . . . . .
13
3 Aim of Study
14
4 Method
15
4.1
Measurement of B71 Frequency Response
. . . . . . . . . . .
15
4.2
Modelling of B71 . . . . . . . . . . . . . . . . . . . . . . . . .
15
4.3
4.2.1
Parameter Values . . . . . . . . . . . . . . . . . . . . .
16
4.2.2
Extension of the Model
. . . . . . . . . . . . . . . . .
18
. . . . . . . . . . . . . . . . . . . . . . . . .
18
The Simulations
4.3.1
Force Variability
. . . . . . . . . . . . . . . . . . . . .
18
4.3.2
Bias Error . . . . . . . . . . . . . . . . . . . . . . . . .
19
4.3.3
At Skull Bone . . . . . . . . . . . . . . . . . . . . . . .
19
5 Results
22
5.1
Measurement of B71 Frequency Response
5.2
Output Variability
5.2.1
5.3
. . . . . . . . . . .
22
. . . . . . . . . . . . . . . . . . . . . . . .
22
Bias Error . . . . . . . . . . . . . . . . . . . . . . . . .
23
At Skull Bone . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
6 Analysis and Discussion
32
6.1
The Models . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
6.2
The Simulations
. . . . . . . . . . . . . . . . . . . . . . . . .
32
6.2.1
Variability . . . . . . . . . . . . . . . . . . . . . . . . .
32
6.2.2
Bias Error . . . . . . . . . . . . . . . . . . . . . . . . .
36
6.2.3
At Skull Bone . . . . . . . . . . . . . . . . . . . . . . .
38
7 Conclusions
42
7.1
Main Points . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
7.2
Continuation
43
. . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Acknowledgments
44
A Calculation of Transfer Function
45
B Model Parameter Values
47
1 Introduction
Hearing impairment and deafness aect a signicant portion of the world's
population today. Precise demographics are dicult to obtain - due in part
to the unwillingness of many to consider themselves as disabled - but existing statistics suggest that a signicant portion of the world's population is
aected. The Swedish agency HRF (Hörelseskadades Riksförbund) reported
statistics in 2009 from CSB (Centrala Statistikbyrån) showing that 17.2%
of Swedish people had qualied themselves as hard of hearing or hearing
hearing impaired or as having impaired
hearing loss ) by CSB's standard. Of these nearly 1.3 million peo-
impaired (hereafter referred to as
hearing
or
ple, approximately 30% use an assistive device such as a hearing aid, and an
estimated 60% could gain benet from the use of one (HRF, 2009). Impaired
hearing can come as a result of congenital defects or damage to the hearing
organs due to disease or trauma and can for many signicantly aect the
quality of life. These statistics show a clear need for hearing aids, and there
are numerous dierent devices and manufacturers available on the market
to assist in improving hearing for those who can and wish to use them. A
relatively small portion of those with impaired hearing are unable to use
the traditional air-conducting (AC) hearing devices, but can gain benet
from the use of a bone-conducting device such as are studied in this work.
Bone-conducting (BC) devices are being increasingly used to assist those
with suitable needs, and the need for improvement and development of these
products is growing as well.
When attempting to determine the type and level of hearing loss in a
patient, a hearing test is performed, normally measuring hearing thresholds.
Hearing thresholds are then used to evaluate a suitable treatment, whether
it be surgery, drugs, taking no action at all or the use of a hearing aid.
The standards for hearing thresholds is called
audiometric zero
and is based
on measurements taken from average normal-hearing young adults. For AC
devices the standards are measured in sound pressure. For BC transducers,
the standards for audiometric zero (ISO, 1994) are given in force, and have
been dened by the use of RETFLs (Reference Equivalent Threshold Force
Levels) and a device called an articial mastoid which simulates the acoustic
properties of the mastoid portion of the skull bone. The force experienced at
the mastoid portion of the skull (where the BC device is normally applied)
is dependent on the mechanical impedance (complex mechanical resistance)
of the subject's skull, by the relationship
Z(jω) =
(1)
Z(jω) (the skin impedance) is the mechanical point impedance of the
seen from outside the skin at the mastoid, v(jω) is the vibrational
where
skull
F (jω)
v(jω)
1 INTRODUCTION
2
velocity and F (jω) is the force produced at the mastoid at a given angular
frequency ω . The variation in individual Z has been shown to be considerable
(Cortes, 2002) and may result in variability in force and velocity produced at
the transducer/skin interface by the BC transducer. A study of the behaviour
of this system is helpful in understanding the signicance and accuracy of
the existing standards in audiometry.
2 Background/Theory
2.1
Biology and Mechanics of Hearing
Human beings and many other organisms on earth use auditory sensing known in their case as hearing - to perceive their surroundings. The ear (See
gure 1) is the primary sensing organ for sound and consists of three parts.
The outer ear lters, reects, amplies, and transmits sound to the middle
ear. It consists of the external cartilage and skin (known as the pinna ) and
the auditory canal, a soft tube which leads to the tympanic membrane, or
ear drum. The middle ear is the air-lled cavity between the eardrum and
the cochlea, and contains the three bones known as ossicles. These act as
mechanical levers driven by the vibration of the tympanic membrane, and
amplify the pressure of the vibrations as they are transmitted to the oval
window, the beginning of the middle ear. The oval window is a membrane
which separates the middle ear from cochlea, which contains the sensory
organ of the inner ear. The cochlea is uid-lled, and the vibrations propagated in this uid stimulate the hair cells of the organ of corti, converting
the mechanical vibrations to electrical action potentials in the hair cells for
transmission via the auditory nerve to the brain for interpretation. In this
sense the organ of corti acts as a transducer, and in humans it has the ability
to receive and transduce sound signals with a dynamic range of 20 − 20k Hz .
The complexity of this organ is considerable, and for the scope of this work
it will suce to say that hearing sensitivity varies signicantly over this frequency range.
The conduction of sound through the outer and middle ear is primarily
via air and the soft tissue from the pinnae to the tympanic membrane, then
by the bones of the ossicular chain and the air surrounding them. This
is however only one path of conduction between the surroundings and the
cochlea. Sound can also travel through the bones of the skull, surpassing
the outer and middle ear entirely. As can be seen in gure 1, the inner ear
is quite deep inside the head, and is surrounded by bone. When the bone
vibrates, the cochlea can be directly stimulated, which produces the same
sensation of hearing that is achieved through air conduction.
This type of sound conduction can be observed when speaking while
occluding the ear canals with the ngers. The percieved volume of one's
own voice is not signicantly aected, as it is transmitted through BC via
the teeth, jaw, hard palate and skull to the cochlea, though the transmission
of low frequencies over high ones is quite prevalent. Unlike the own voice,
however, the majority of sound reaches the cochlea almost exclusively via
air conduction, which means that problems with the outer or middle ear can
result in impaired hearing.
2 BACKGROUND/THEORY
Figure
1:
The
anatomy
http://www.guadalupe-ec.org/ )
4
of
the
ear.
(Image
taken
from:
2 BACKGROUND/THEORY
2.2
5
Hearing Loss
Hearing loss can be loosely grouped into: sensorineural, conductive, and
mixed. Sensorineural hearing loss is due to impaired function of the inner
ear, auditory nerve, or higher centra in the brain. If the sensitive hair cells
in the organ of corti are damaged or defective, or if there is a problem with
neural transmission or processing of the electrical signals produced therein,
the impairment is considered sensorineural. This can in certain cases be
treated by a cochlear implant, which is a device that directly stimulates
nerve cells in the cochlea via electrodes, hence transducing the auditory
signal from mechanical waves to electrical signals. Pure conductive hearing
loss is characterised by a functioning sensorineural system, but with impaired
acoustic/mechanical conduction of sound to the inner ear. This can depend
on a number of factors such as occlusion of the hearing canal, damage or
deformation of the middle ear, tumours, and obstruction of the oval window. Mixed hearing loss is any combination of conductive and sensorineural
hearing loss.
The treatments for conductive hearing loss vary and can include surgery
to physically alter the problematic region of the auditory pathway. A common method of treatment is the amplication of incoming sound to compensate for the problematic attenuation. This can be done by placing an
AC loudspeaker device directly in the ear canal. These devices and their
bulkier body-worn and table-top predecessors have been used since the early
20th century, before which a commonly used method was passive mechanical
amplication of sound with an ear horn.
With some types of conductive and mixed hearing loss, the use of bone
conduction to transfer sound to the cochlea is preferable to air conduction.
These include patients for whom the obstruction/xation of the ear canal is
undesirable or impractical because of congenital malformation or chronic infection or eczema of the middle and outer ears, or those who have such
impaired conduction in the middle ear that the gain obtained from airconduction devices cannot compensate for the attenutation.
2.3
Audiology
When a patient is suspected of having a hearing impairment, they visit an
audiologist to determine the severity and type of hearing loss they have. The
audiologist performs an audiometric evaluation, which is normally a test of
hearing thresholds at a number of dierent pure-tone frequencies within the
range of human hearing. A complete pure-tone audiometry consists of testing
hearing thresholds through air conduction and bone conduction.
Before the testing is done, the equipment is calibrated according to the
ISO 389 series standard, and the patient is informed on how to indicate that
they hear each test tone. They are placed in an anechoic sound insulated
2 BACKGROUND/THEORY
6
test room where they have visual contact with the tester, and are tted with
insert or alternately supra- or circumaural headphones. The tester sends an
audible pure tone at 1000 Hz to one of the headphones, then decreases the
level of the tone in 10 dB steps until the patient no longer indicates that
they can hear it. The level is then increased in 5 dB steps until the patient
can hear the sound again. This procedure is repeated until the patient has
responded on the same threshold level on two out of two, three, or four ascents (BSA, 2002). This is the threshold level of hearing for that frequency.
The process is repeated with tones of frequencies 2000, 4000, 8000, 500, and
250 Hz . If needed, the intermediate frequencies 750, 1500, 3000, and 6000 Hz
can be tested as well. Retesting at 1 kHz is done for the rst ear, and if
there is an acute dierence of more than 5 dB in threshold value, the other
frequencies are retested as well. After this process is carried out for both
ears, the bone conduction test is performed.
The procedures for bone conduction audiometric testing are similar or
identical to the one for air conduction, with two important dierences:
• the frequencies tested are usually limited to 500 − 4000 Hz (BSA,
2002), and
• the need for masking becomes an important consideration.
The reduced range of frequencies depends on several factors. The standard BC hearing aid used for audiometery is the Radioear B71. As with
other BC transducers, the B71 demonstrates high levels of total harmonic
distortion (THD) at high signal levels and also at low frequencies (Stenfelt
and Håkansson, 2002). Since THD is a measure of the ratio of total harmonic frequency power to fundamental frequency power, a high THD means
signicant overtone presence. This can lead to inaccurate measurements
of the hearing threshold at frequencies with high THD, as the harmonic
overtones could become audible at lower signal levels than the fundamental.
An additional reason for not measuring BC thresholds at frequencies below
500 Hz is the contribution of vibrotactile sensation. This refers to the ability to sense vibration rather than hear it, and the vibrotactile thresholds at
low frequencies are such that vibrotactile sensation could give more acute
hearing thresholds (as low as 25 dB hearing loss at 250 Hz )(Stenfelt and
Håkansson, 2002). At higher frequencies, the performance of the B71 is also
limited and the accuracy of the test becomes compromised. Above 2 kHz ,
the airborne sound radiation from the transducer housing can become sufcient to contribute to hearing sensation. This may result in inaccurately
acute thresholds, and it is recommended by the British Society of Audiology
that the ear canal of the ear being tested is occluded at frequencies of 3000
and 4000 Hz (BSA, 2002).
2 BACKGROUND/THEORY
7
With bone-conduction, there can be a signicant amount of cross-hearing
(between the two ears) due to transmission of the vibration through the
skull bone to the contralateral cochlea. Whereas the transcranial attenuation
sound with AC headphones can be signicant (from 40−80 dB BSA (2002)),
bone conduction may cause as little as 0 − 20 dB attenuation (BSA, 2004),
and the sound can even be percieved as louder on the contralateral side
than the ipsilateral (Håkansson et al., 2010). Since threshold dierences
between the ears can far exceed 20 dB, the sound may be detected by the
opposing ear before the one being tested. When single-ear threshold testing
is desired, this necessitates masking of the contralateral ear with narrowband noise to elevate that ear's threshold. The procedures for masking will
not be explained here, but can be found in the BSA guide referenced here
(BSA, 2002). Standards for calibration levels can be found in ISO 389.
When AC and BC threshold tests have been done, the results are plotted
in an audiogram, which shows the hearing threshold at each tested frequency
in decibel hearing level (dBHL) relative to the standard audiometric zero
specied in ISO 389. Audiometric zero represents the threshold of hearing
for an average normal hearing person. The determination of audiometric
zero for bone conduction uses a method involving an articial mastoid, and
is described below. There are several methods for determining where the
hearing thresholds lie, but all should give a set of data showing the BC
thresholds and one showing the AC thresholds. An example of an audiogram
is seen in gure 2.3. By analysing the relation between these thresholds, the
type of hearing loss can be roughly determined. A large and uniform gap
between the AC and BC thresholds with BC thresholds being lower (more
sensitive) indicates conductive hearing loss, while the coincidence of higher
AC and BC thresholds can suggest that a hearing loss is sensorineural. Some
diseases or conditions show a frequency-dependent hearing loss, and they can
be diagnosed by the help of an audiogram as well.
2.3.1
Calibration for BC Audiometry
As mentioned above, before an audiometric test battery is conducted, it is
essential that the equipment is calibrated so that audiometric zero (seen
in gure 2.3 as the line marked 0 dB) represents the hearing thresholds of
the average otologically normal hearing person. With AC, the calibration
can be done by directly measuring the sound pressure at the output of the
headphones and adjusting the signal strength accordingly. For BC devices,
the force level at threshold cannot be measured directly without specialized
equipment, and the standard measure of audiometric zero is a force produced
by the BC device (normally a Radioear B71) on an articial mastoid (AM)
B&K type 4930, which is designed to indirectly measure the force output of
the BC transducer. A correction is applied to this measured data to take into
account that the force gauge is placed under the rubber pad of the B&K 4930.
2 BACKGROUND/THEORY
8
Figure 2: An example of an audiogram for BC and AC thresholds in one
ear.(Image taken from: http://www.osha.gov )
This corrected force is known as the reference equivalent threshold force level
(RETFL) and is dened as the force output on an AM when applying the
same electrical input signal that produces a threshold-level sound when the
BC device is attached to an average otologically normal person. Once the BC
device is calibrated, the dB dierence in signal strength between audiometric
zero and the subject's threshold can be found and plotted in an audiogram.
From equation 1, it can be seen that the force produced is dependent on
the mechanical point impedance Z of the load. If the impedance of two
loads such as an articial mastoid and a human mastoid diers, the output
force for a given input signal will dier as well, dependent on the electrical
and mechanical properties of the BC device. It is known that the standard
impedance for articial mastoids diers from that of the average human
mastoid. Consequently the force output may dier at the human mastoid and
the articial mastoid, and this is why the standard is referred to as a reference
equivalent force level. This may be a cause of uncertainty in audiometric
threshold determination, as the reference thresholds for audiometric zero
and the measured thresholds are taken from dierent subjects. The error
caused by these dierences will be unknown at each audiometric test, but
a knowledge of the potential error is still useful in the interpretation of
results. The variability in force output due to variability in human mastoid
2 BACKGROUND/THEORY
9
impedances, and the dierence in force output on an AM and a human
mastoid are therefore of interest.
2.3.2
Sources of Error
The accuracy of the audiometric measurements is important to enable proper
analysis of hearing loss. Sources of error as well as intersubject and test-retest
variability must be considered and accounted for. Conformance to standards
ensures some accuracy, however, some sources of error and variability remain.
These include:
• Position of device - small variations in placement on the mastoid can
correspond to large variations in impedance.
• Contact pressure variability.
• Subject response error - many factors such as attentiveness, breath-
ing and heartbeat sounds, and understanding of instructions may contribute.
• Operator error.
• Ambient noise contribution.
• Calibration error.
The importance of being able to account for threshold variability in audiometry increases when one considers the worst-case scenario, where the
dierent errors and variabilities add up. An analysis of the total possible
error and condence intervals for determination of hearing thresholds by AC
and BC requires a quantitative knowledge of the individual sources of error.
As was adressed above, there are possible sources of variability and bias errors in the determination of BC thresholds that are known to exist, but are
unknown in magnitude. A better quantitative knowledge of these factors is
hence of importance to the eld of audiology.
2.4
Bone Conduction Hearing Devices
BC devices, though far less common than AC devices have come to be in
common use in the last few decades. For those who desire or require a BC
device, there are two viable alternatives and one currently under development. The rst and oldest type of BC device is the transcutaneous (through
the intact skin). These devices consist of a transducer xed in a casing which
is pressed against the skull, normally behind the ear at the mastoid portion
of the temporal bone. The device is held in place by a steel spring or a soft
headband which provides the correct contact pressure. The second type is
percutaneous (through the skin), and requires an implanted skin-penetrating
2 BACKGROUND/THEORY
10
titanium screw. The screw is most commonly placed and anchored in the
mastoid portion of the temporal bone about 55 mm behind the pinna, and
after being osseointegrated is tted with a post which protrudes from the
skin to provide an attachment point for the transducer. The device is attached to the implant by a snap coupling to allow for easy release so as
to minimize damage to the device and the implant upon accidental impact.
The eectiveness of direct bone stimulation together with the added comfort and aesthetic appeal of a headband-free device have made the BAHA
(Bone Anchored Hearing Aid) the preferable device for most. Equally as
important is the increased quality of the conducted sound at lower power
consumption made possible by the direct transmission of vibrations into the
skull. The hearing device currently under development is the subcutaneous
Bone-Conduction Implant (BCI), which will use an implantable transducer
that is powered transcutaneously by electromagnetic induction. This type
of device will provide the same benets as BAHAs, but with the lack of a
permanent opening in the skin for the titanium abutment.
2.4.1
The B71
The BC device used in most audiometry is the Radioear B71 (shown in gure
3). The device dimensions are 31 × 18 × 18 mm, and it has a total weight
of 22.3 g, not including the headband. It is held in place by a steel or soft
fabric headband, which provides a contact pressure of approximately 5.4 N
across a contact area of 2.0 cm2 . The exterior of the B71 consists of a plastic
casing with two terminals on one short end for the input electrical signal.
The round protruding portion of the casing is the contact surface which is
pressed against the mastoid. The halves of the housing are held together by
three screws, and the transducer inside is attached to the back of the casing
with two screws. Figure 3(a) and 3(b) shows the casing and the transducer
when removed from the casing.
The transducer is of variable-reluctance type, and consists of a magnetic
armature suspended from the casing by the compliant side arms of a sti
metal plate (visible between the screws in gure 3(b)). The electrical signal
passes through coils of wire which are wrapped around the armature, inducing a magnetic ux in the magnetic circuit consisting of the armature and
the metal plate. The resultant force generated across the air gap in the circuit causes a deection of the suspended plate, which manifests as harmonic
vibrations when an alternating electrical signal is applied. This vibration is
propagated through the plastic casing and into the skull of the user as sound.
2.5
Modelling and Simulation
For system-based engineering applications such as this one, analysis and
quantication are needed at all stages of development. This analysis gener-
11
2 BACKGROUND/THEORY
(a)
(b)
Figure 3: (a) The B71 transducer with and (b) without its casing.
ally requires that system behaviour be quantied so that an objective comparison can be made between dierent decisions in the development process.
The desired quantities to be extracted can be dicult or inecient to measure directly (or impossible if the system does not yet exist) due to the need
for equipment and subjects, time constraints, setup logistics, system complexity, and measurement and equipment error. An alternative to the direct
measurement of parameters in a system is the use of a model for simulation. With the creation of an appropriate model a particular system can be
simulated, providing the freedom to vary parameters of interest and observe
the resulting changes in behaviour. An important benet of simulation is
the ability to simplify the system and isolate the outputs of interest. This
and other benets can far outweigh the drawbacks, provided that the model
is well designed and consideration is taken of the potential contributions to
system behaviour that are removed or simplied.
2.5.1
Electrical/Mechanical Analogies
The mathematical treatment of simple mechanical systems involves the use
of linear dierential equations to express the relationships between force,
acceleration, velocity, and physical characteristics such as mass and compliance. Interestingly, these dierential equations have exact analogies in the
electrical domain and as a consequence, mechanical systems can be simplied and modelled as electrical systems and vice versa. These analogies are
utilized in this work to model the electromechanical system of the B71 as a
relatively simple electrical system.
There are two common analogues in the electrical domain, both of which
start by dening potential and current as electrical analogues to mechanical
quantities. In this work, force is represented by potential and velocity is
represented by current. It will be demonstrated here how the analogue to
mass is derived from these, then additional relevant analogues are presented
in table 1.
2 BACKGROUND/THEORY
12
Table 1: Mechanical-Electrical analogue quantities
Mechanical
Notation
Electrical
Notation
Force
F
Potential
u
Velocity
v
Current
i
Compliance
cm =
1
F
R t2
t1
m=
Mass
Damping
v(τ )dτ
F
Capacitance
Inductance
dv
dt
Rm = ℜ( Fv )
Resistance
C=
1
u
R t2
t1
L=
i(τ )dτ
u
di
dt
R = ℜ( ui )
Newton's second law can be written as:
F =m·a=m·
Upon replacing the force
F
dv
dt
(2)
v with their electrical equivm is equivalent to inductance
and the velocity
alents, it becomes apparent that the mass
L
u=L·
di
dt
(3)
The analogies for capacitance and resistance are derived similarly by using
Hooke's and Ohm's laws respectively.
As in the electrical domain, the relationship between the force and the
velocity at a given frequency is such that their quotient yields the
by equation 1, where Z denotes the complex impedance.
impedance
Note that the
calculation of resistance in table 1 is done by taking the real part of this
quotient.
When the force and velocity are taken at the same point,
Z
is
referred to as driving-point impedance, which in this work will be referred
to simply as impedance.
2.5.2
Two-Port Models
One way to model an electrical system is using a two-port network.
An
advantage of this model is that the parameters can be determined by direct measurement without any knowledge of the components of the system.
13
2 BACKGROUND/THEORY
i1
+
V1
-
Z11
Z21
Z12
Z 22
i2
+
V2
-
ZL
Figure 4: A "black box" two-port network with a load ZL on the output
side.
Provided that there are an output port and an input port (each with two terminals) satisfying the condition that the same current enters and leaves each
port, the system can be considered a black box characterised only by four
network parameters. The parameters themselves are determined by relationships between measured quantities at the ports, and can be impedances,
admittances, or hybrids of the two. Figure 4 shows a two-port depiction of
a linear electrical system using impedances as network parameters.
Since the B71 is a linear system composed of passive components, it can
be and has in fact been modeled as a two-port network (Cortes, 2002). For
the purposes of this work, the two-port model was undesirable to use as it
does not allow for the manipulation of individual components in the system.
2.5.3
Lumped Parameter
An alternative method is to model the transducer as a network of its individual electrical components. This allows for the individual manipulation and
if desired, reconguration of the component quantities. This type of model
is more exible than a two-port model, and was suitable for use in this work.
With this type of model, computer software such as SPICE can be used to
R can be used if the transfer
solve for individual quantities, or MATLAB
function between known and desired quantities is rst determined.
3 Aim of Study
The aim of this work is to use a model of the B71 in conjunction with
measured impedance data to simulate the behavior of this BC device in terms
of its state variables force, acceleration, and power at the mastoid portion
of the human skull. Of particular interest is the variability in output due to
variability in the load, and the consequences and causes of this behavior.
Questions that will be addressed in this study:
• How does the variability in output dynamics relate to the variability
of human mastoid impedances?
• What is the bias error due to calibration with an articial mastoid?
• What is the size and variability of the output quantities under the skin
at the mastoid?
4 Method
4.1
Measurement of B71 Frequency Response
The frequency response function Fout /uin was measured for the Radioear
B71 device #86-5. An Agilent 35670A signal analyzer was used for signal
generation and measurement, and a B&K Articial Mastoid type 4930 (Serial
#2278234) was used as the load. The stimulating signals uin used were a
logarithmic sweep of 401 single-frequency sinus signals ranging from 100 −
10k Hz and an averaged series of white noise measurements with a frequency
range from 100 − 12.8k Hz . Both signals had an RMS voltage of 0.5V . The
signal was sent as input to channel 1 as well as to the terminals of the B71.
The B71 was placed in the B&K Articial Mastoid under a pressure of 5.4
N. The output force signal of the B&K AM was sent to channel 2 of the
signal analyzer, and the frequency response function
Fout
uin
(4)
was displayed in dB as a function of frequency. The data was imported to
MATLAB along with the 401-point frequency vector, and a correction for
the frequency dependent force sensitivity of the B&K 4930 AM was applied
to the data. The measured frequency response is shown in gure 9.
4.2
Modelling of B71
The model of the B71 used in this work is adapted from Håkansson et al.,
1986, and reworked (Håkansson, 2010, personal communication). A schematic
is shown in gure 5. The electrical and mechanical parts of the transducer
are shown as lumped parameters, and the load which in this case is the mastoid is shown as an unknown impedance. On the electrical side, the source is
modeled as an ac voltage source and the transducer's coil ohmic resistance,
coil inductance, and frequency-dependent resistance of the magnetic core
losses are shown as separate components.
The transduction is represented by two dependent voltage sources, which
model the interaction between the velocity of the suspended plate and the
current throught the coils. A transduction constant g relates the velocity v
on the mechanical side to the current i on the electrical side. The compliance
and damping of the transducer suspension are represented in series as C1 and
R1 . The total mass of the armature, bobbins, and wire are represented by
m1 . The casing itself has some compliance, mass, and damping and these are
represented by C2 , m2 , m3 , and R2 respectively. The mass of the casing is
16
4 METHOD
R0
L0
R1 C1
•R
i v
Ug
+
-
g•v +-
+
-
g •i
m1
m2
C2
R2
m3
+
Fout
-
Figure 5: The lumped-parameter model of the B71 with input voltage source
Ug and load impedance ZL
divided among two components as part of the casing is resonant with its own
compliance, and the rest is more closely connected to the load. The force
and velocity at the interface between the casing and the skin of the subject
are represented in the circuit by the voltage and current over the load. By
calculating the transfer function in equation 4 in terms of the components,
the quantities of force, acceleration, velocity, and power at the load can be
estimated. The behavior of this function is best understood by a qualitative
description of the circuit, and the calculation of the transfer function can be
seen in Appendix A.
Component
Mass(kg)
Bobbin,Coils and Magnet
.01473
Plate
.00217
Casing (Inner half)
.00196
Casing (Outer half)
.00200
Screws (Plate to Magnet)
.00023
Screws (Casing and Vibrator) .00150
Table 2: Component masses for B71 (Serial #86-5)
4.2.1
Parameter Values
Once the layout of the model is determined, the values of the lumped parameter circuit elements are to be assigned so that the model's performance
will closely resemble that of the device being modeled in a simulation.
The lumped parameters that are most easily measured are all the parameters on the electrical side of the circuit - with the exception of the frequencydependent resistance - and the masses on the mechanical side. The masses
of the transducer components as measured on an OHAUS Dial-O-GramR
balance scale are listed in table 2. The values of parameters on the electrical side are taken from the two-port parameter Z11 measured for the same
ZL
17
4 METHOD
device by Cortes (2002). This parameter is a measure of the impedance
of the electrical side of the transducer, and the inductance could be found
from the slope of the magnitude, the resistance from the minimum value of
the magnitude, and the frequency-dependent resistance from the phase and
knowledge of the impedance.
The distribution of the masses to the parameters m1 , m2 , and m3 as
well as the determination of the compliances and damping is determined by
a practical understanding of the physical layout of the device along with
analysis of the circuit and comparison to actual device performance. Firstly,
the mass of the transducer is assigned to m1 . The remaining mass - that
of the casing, screws, and the suspended plate is distributed between m2
and m3 . This distribution as well as the determination of the damping in
the system is done by analysis and tting of the results of simulation to the
measured transfer function of the B71, shown in gure 9. As the measured
force output in the gure is made with a B&K Articial Mastoid type 4930
(Serial #2278234) as the load, the load used in the MATLAB simulation is
measured impedance data of the same device.
In gure 9 there are three clearly visible peaks at approximately 400, 1450,
and 3650 Hz . These peaks correspond to frequencies at which there is electromagnetic or mechanical resonance in the system, and can be used to
determine appropriate component values. In an electric circuit, resonance
can be seen where there is a combination of inductors and capacitors in series or in parallel, and in cases with suciently little damping the resonant
frequency can be calculated to be
fr ≃
1
√
2π LC
(5)
where L is the value of the inductance in Henry and C is the capacitance in
Farads. On the mechanical side, the resonance then depends on the masses
and compliances of the system. The B71 has its maximum force output at
the 400 Hz resonant frequency, which corresponds to resonance between the
transducer mass m1 with the compliance C1 . The second resonant frequency
occurs as an interaction between masses m2 and m3 and the compliance and
mass of the load, and the 3.7 kHz peak from resonance due to the compliance
C2 of the casing and its mass m2 . Using the measured values for masses and
frequencies, the compliances and damping can be estimated. With a numeric
approach in MATLAB to nd the best t for the force output curves, the
distribution of casing weight between m2 and m3 as well as values for the
damping constants are found. Figure 9 shows the simulated curve of output
force per volt input with the articial mastoid impedance as load data, along
with the measured transfer function Fout /uin described in section 4.2. Once
the dimensions of the model have been satisfactorily determined, the model
can be used to study the output when loaded with dierent data. This model
can thus be used to address the questions presented in section 3.
18
4 METHOD
R0
L0
R1 C1
•R
i v
Ug
+
-
g•v +-
+
-
g •i
m1
m2
C2
R2
m3
Rt2 mt2
ms
+ C
s
Fskin
Rs
-
+
Fskull
-
Ct1
Rt1
Rt3
mt3
Figure 6: The model of the B71 connected to a model of the skull bone via
skin parameters Cs , ms and Rs
4.2.2
Extension of the Model
To determine the eect of the force, acceleration, and power incident on
the skull bone underneath the skin, the impedance of the skull needs to be
separated from that of the skin. First a model of the skull impedance through
a titanium implant is adapted from Håkansson et al., 1986 by removing the
compliance C0 directly associated with the bayonet coupling between the
transducer and the titanium post. An assumed model of the skin with a mass
component in series and a compliance and damping component in parallel
is connected to this model, and the combination is connected to the model
of the B71 (seen in gure 5). The complete model is shown in gure 6.
Estimation of the values for the skin mass, compliance and damping is done
in two steps:
First, the measured BC impedances seen in gure 7 are assumed to be
representable as a three-parameter model as seen in the work of Håkansson
et al. (1986). These parameters are estimated for each subject by a division
operation in MATLAB corresponding to a least-squares approximation. The
median of the estimated three-parameter impedances and the median of
the actual mechanical point impedances are compared in gure 14. Next,
the input impedance ZS of the combined model (looking towards the skull
from outside the skin, at Fskin in gure 6) is calculated while sweeping the
parameters Cs and ms for the skin. ZS is compared to the three-parameter
model for each subject, and the values of Cs and ms which minimize the
rms error between the two are determined for each subject, and stored as
the skin compliance and mass. The damping Rs used for each subject is the
same as for the three-parameter model of the BC impedance.
4.3
4.3.1
The Simulations
Force Variability
To determine the output force variability's dependence on variability in load
impedance, the B71 model was loaded with the measured mechanical point
impedance (skin impedance at the mastoid) of 30 dierent subjects in the
frequency range 0.1−10 kHz . The data was obtained from Cortes (2002) and
Ct3
19
4 METHOD
the group consisted of 30 normal hearing subjects - 18 males and 12 females
with ages between 22 and 51 and a mean age of 30.6 years (Cortes, 2002,
pg. 2). An analysis of the error in these measurements can be found in the
work (Cortes, 2002, pg. 5). Figure 7 shows the magnitude and phase of the
measured impedances. The complex impedances represented in MATLAB as
vectors were used as the load in the model, and the transfer function Fout /uin
was calculated at each of 801 logarithmically spaced frequencies with a range
from 100 − 10000 Hz . Please note that a model generator voltage of 1 V
was used in all simulations, hence Fout /uin may be referred to simply as Fout
and the transfer function as output force. The acceleration at the skin is
determined by dierentiation of the velocity through mulitplication with the
term jω
a(jω) = (jω) · v(jω) = (jω) ·
Fout (jω)
ZS (jω)
(6)
The apparent power output at the skin is also determined using the output
force and impedance data by
Sapp (jω) = |S(jω)| =
4.3.2
2 (jω)|
|Fout
|ZS (jω)|
(7)
Bias Error
To determine the bias error in force threshold measurements due to AM
impedance, the force output of the model was calculated using the impedance
of the B&K Articial Mastoid type 4930 (Serial #2278234) as the load. This
force is compared at each frequency to the force output from the 30 subjects
as calculated in 4.3.1.
4.3.3
At Skull Bone
The estimated parameters Cs , ms , and Rs for skin compliance, mass and
damping were used in the combined model (gure 6), and the transfer function from equation 4 was evaluated for Fskull . The parameters for the
adapted skull model and for the B71 model were unchanged. From the
transfer function, acceleration and power were calculated in the same way
as described in 4.3.1.
4 METHOD
20
50
Magnitude [dB(Ns/m)]
45
40
35
30
25
20
15
125
250
500
1k
2k
4k
8k
2k
4k
8k
Frequency [Hz]
(a)
80
60
Phase [Degrees]
40
20
0
−20
−40
−60
−80
125
250
500
1k
Frequency [Hz]
(b)
Figure 7: (a) Magnitude of mastoid mechanical point impedance for 30 subjects, and the median of the magnitudes at each point. Magnitude in dB
relative to 1 Ns/m. (b) Phase of the same impedances also including median.
21
4 METHOD
Median ZS
50
Measured ZAM
Standard ZAM (IEC 60318−6)
Magnitude [dB(Ns/m)]
45
40
35
30
25
20
125
250
500
1k
2k
4k
8k
Frequency [Hz]
Figure 8: The solid line shows the magnitude of the median measured skin
impedance from Cortés (2002). The dashed line is the measured impedance
of the B&K Articial Mastoid type 4930 (Serial #2278234), and the circles
show the IEC standards for articial mastoid impedances.
5 Results
5.1
Measurement of B71 Frequency Response
The measured frequency response of the force output for the B71 #86-5 is
plotted in gure 9. Note that the x and y axes are both logarithmic and that
the tick markings on the x-axis correspond to the common test frequencies
in audiology applications as well as some additional frequencies of interest.
130
Measured Force Output (AM as load)
Modelled Force Output (ZAM) as load)
Magnitude [dB(µN/V)]
120
110
100
90
80
70
60
125
250
500
1k
2k
4k
8k
Frequency [Hz]
Figure 9: Measured magnitude of the force output of the B71 using AM B&K
4930 as the load, and force output of MATLAB simulation with lumpedparameter model and AM impedance data.
5.2
Output Variability
The transfer function Fout /uin for the B71 when loaded with the measured
skin impedances (gure 7(a)) is shown in gure 11(a) along with the median
force. The corresponding accelerations are shown in gure 12(a), and the
apparent power out in gure 13(a).
The variability in impedance, force, acceleration, and apparent power are
presented as standard deviations (based on the quadratic dierences between
the mean values and measured values in dB) in table 3. They are also plotted
5 RESULTS
23
in gure 10. Though standard deviation is calculated with reference to the
mean, the median was chosen for displaying the results in this work. This is
for simplicity as, unlike the mean, the median value is the same for the data
and their dB values.
Measure
Min STD [dB]
Max STD [dB] Mean STD [dB]
Skin Impedance
2.08
2.79
2.44
Force
0.06
4.06
1.71
Acceleration
0.02
4.91
1.60
Power
0.13 (dB Power) 3.66 (dB Power) 1.39 (dB Power)
Table 3: Intersubject variability measured in standard deviation (STD).
5.2.1
Bias Error
The dierence in the transducer's mechanical state variables when loaded
with the AM and with the mastoid impedances is seen in gures 11(b)13(b). The dierence in force, acceleration and power between the AM
and the median subject ranges from zero to more than twice the standard
deviation of intersubject variability.
5.3
At Skull Bone
The values for the force at the skull bone for the 30 subjects including the
median are shown in gure 15(a). Figure 17(a) shows the magnitude of the
force on the skull bone of the 30 subjects and their median is shown together
with the median of the force at the skin. The ratio between the median forces
are shown in gure 17(b)
The estimated three-parameter model of the skin impedance, and the
subsequent three parameters used to model the skin's contribution to the
model including the extended skull part were found to be very similar, with
the mean compliance diering most (approximately 5%). The averages of
the three parameters used to estimate the measured skin impedance were
mSest = 7.6 ∗ 10−4 , CSest = 4.2 ∗ 10−6 , and RSest = 14.0. The mean of the
parameters used in the extended model to characterise the skin alone were
mS = 7.6 ∗ 10−4 CS = 4.0 ∗ 10−6 and RS = 14.0.
5 RESULTS
24
5
Skin Impedance
Force
Acceleration
Power [dB Power]
4.5
Standard Deviation [dB]
4
3.5
3
2.5
2
1.5
1
0.5
0
125
250
500
1k
2k
4k
Frequency [Hz]
Figure 10: Standard deviation of impedance, force, acceleration, and power
at the skin of the 30 sub jects.
8k
25
5 RESULTS
130
Magnitude [dB(µN/V)]
120
110
100
90
80
70
60
50
125
250
500
1k
2k
4k
8k
1.5k 2k
3k 4k
6k 8k
Frequency [Hz]
(a)
130
Magnitude [dB(µN/V)]
120
110
100
90
80
70
60
50
125
250
500
750 1k
Frequency [Hz]
(b)
Figure 11: (a) Magnitude of the output force at the skin of 30 subjects.
Force is displayed in dB relative to 1 µN per Volt input. (b) Median output
force at the skin of 30 subjects and output force with the articial mastoid as
the load. The shaded area and the error bars show the range of the median
force plus/minus the standard deviation.
26
5 RESULTS
50
Magnitude [dB(m/s2/V)]
40
30
20
10
0
−10
−20
−30
125
250
500
1k
2k
4k
8k
1.5k 2k
3k 4k
6k 8k
Frequency [Hz]
(a)
50
Magnitude[dB(m/s2/V)]
40
30
20
10
0
−10
−20
−30
125
250
500
750 1k
Frequency [Hz]
(b)
Figure 12: (a) Magnitude of the output acceleration at the skin of 30 subjects. Acceleration is displayed in dB relative to 1 m/s2 per Volt input.
(b) Median magnitude of output acceleration at the skin of 30 subjects and
output acceleration with the articial mastoid as the load. The shaded area
and the error bars show the range of the median acceleration plus/minus the
standard deviation.
27
5 RESULTS
−10
Magnitude[dB Power(W/V2)]
−20
−30
−40
−50
−60
−70
−80
125
250
500
1k
2k
4k
8k
Frequency [Hz]
(a)
−10
Magnitude [dB Power(W/V2)]
−20
−30
−40
−50
−60
−70
−80
−90
125
250
500
750 1k
1.5k 2k
3k
4k
6k
8k
Frequency [Hz]
(b)
Figure 13: (a) Magnitude of the apparent power output at the skin of 30
subjects. Power is displayed in dB power relative to 1 W per Volt2 input.
(b) Median apparent power at the skin of 30 subjects and with the articial
mastoid as the load. The shaded area and the error bars show the range of
the median power plus/minus the standard deviation σ .
5 RESULTS
28
55
Median of Estimated Three−Parameter Impedances
Median of Measured Impedances
Magnitude [dB(Ns/m)]
50
45
40
35
30
25
20
125
250
500
1k
2k
4k
8k
Frequency [Hz]
Figure 14:
The magnitudes of the median impedances from the three-
parameter estimated model and measured skin impedances from Cortes,
2002.
5 RESULTS
29
140
130
Magnitude [dB(µN/V)]
120
110
100
90
80
70
60
50
40
125
250
500
1k
2k
4k
8k
1.5k 2k
3k 4k
6k 8k
Frequency [Hz]
(a)
140
130
Magnitude [dB(µN/V)]
120
110
100
90
80
70
60
50
40
125
250
500
750 1k
Frequency [Hz]
(b)
Figure 15: (a) The dB magnitude of the force on the bone at the mastoid
of 30 subjects and their median. (b) Median force at the bone and region
encompassing plus/minus one standard deviation.
5 RESULTS
30
30
Magnitude [dB(m/s2/V)]
20
10
0
−10
−20
−30
−40
−50
125
250
500
1k
2k
4k
8k
Frequency [Hz]
(a)
20
Magnitude [dB(m/s2/V)]
10
0
−10
−20
−30
−40
−50
125
250
500
750 1k
1.5k 2k
3k
4k
6k
8k
Frequency [Hz]
(b)
Figure 16: (a) The dB magnitude of the acceleration on the bone at the
mastoid of 30 subjects and their median. (b) Median acceleration at the
bone and region encompassing plus/minus one standard deviation.
31
5 RESULTS
Force and Acceleration Magnitude [dB]
140
120
100
80
60
40
20
0
Median Force at Skull
Median Force at Skin
Median Acceleration at Skin
Median Acceleration at Skull
−20
−40
−60
125
250
500
1k
2k
4k
8k
2k
4k
8k
Frequency [Hz]
(a)
Skin Attenuation (Fskin−Fskull)[dB]
12
10
8
6
4
2
0
−2
−4
125
250
500
1k
Frequency [Hz]
(b)
Figure 17: (a) The dB magnitude of the force and acceleration outputs at
the skin and at the skull bone per volt input for the B71 # 86-5. (b) The
dB force dierence across the skin Fskin [dB]-Fskull [dB]
6 Analysis and Discussion
6.1
The Models
The lumped-parameter models used to simulate the transducer and load
are fairly accurate, as shown in gure 9. The basis for the accuracy of the
transducer model is this comparison to the measured output force per volt
and the average force dierence over the entire range is less than 2 dB. The
average force dierence in the frequencies above 4 kHz is in the order of 5
dB. The accuracy of the model in the upper frequencies is therefore lesser
than between 0.3 and 4 kHz, where the average error is 0.3 dB, which can be
considered negligible. The tting of the model parameters to the measured
output force per volt input of the transducer uses only one set of measured
impedances for the AM, and one set of measured force data. As is discussed
below, AM impedance varies with a number of conditions including how
recently it has been calibrated.
The validity of this model may therefore be greatest when it is used
to produce relatively quantiable data and not absolute quantities. The
comparison of variability in load impedance to that of output state variables
such as force and acceleration is a useful application for this model, while
it may be less suitable for determining absolute quantities such as the peak
force produced. The model can also be used to determine the eects of
altering parameter values, or introducing new components into the system
and comparing the behavior to a control simulation.
The extension of the model to include the model of the skull also has the
greatest validity when used to compare dierent simulation results to one
another. The adoption of three parameters to model the skin impedance was
done with a minimization of rms dierence over the range 1.3 − 7.5 kHz only.
This was done as the mass eects of the whole skull determine the curvature
of the skin impedance at the lower frequencies, and this mass could not be
included in a three-parameter model. Consequently, the extended model
may have a lesser validity under 1 kHz. As the B71 has limited performance
at the low end of it's frequency range, the accuracy of the model may not
be critical in the low frequencies.
6.2
6.2.1
The Simulations
Variability
The variability (expressed in terms of standard deviation or STD ) of the
force, acceleration, and power varies substantially over the simulated range
compared to the load impedance. For example, table 3 shows that the standard deviation of the acceleration has a maximum of 4.91 dB, which corresponds to a range with a maximum value of nearly 20 dB, and a minimum
value of 0.02 dB. The STD's of the force and power vary similarly, in con-
6 ANALYSIS AND DISCUSSION
33
trast to that of the load impedances, which is quite constant over the entire
frequency range. The standard deviation above and below the median is represented by the shaded region in gures 11(b)-15(b), but may be interpreted
more accurately by the size of the error bars in regions with large slope.
The resonance frequency of the skin impedances as well as the the lower
two resonant frequencies of force, acceleration, and power at the skin have
signicant variability as well. The highest resonance frequency in the output
force, acceleration, and power is relatively constant for all subjects. The
qualitative description of the contributors to each resonance given in section
4.2.1 are simplications, as can be seen from the dierence between the measured resonant frequencies and those obtained using the lumped parameter
values and equation 5. The impedance of the load apparently contributes
substantially to the rst resonance frequency as well as the second one as
was mentioned above. The constancy of the third (highest) resonant frequency indicates independence of the variability in load impedances, and
is consistently found at ≈ 3.75 kHz for the output force, acceleration, and
power.
As the successful calibration of an audiometer to absolute zero gives a reference that is based on an average of a group of normal-hearing individuals,
it may be assumed that the error due to intersubject variability is negligible.
When force thresholds are determined for an individual, however, the uncertainty is as large as the variability in force seen in gure 11(a). Under the
assumption that other sources of error such as those listed in section 2.3.2 are
ignored, this alone can still account for up to 10 dB error at some frequencies.
Another source of error that should be mentioned here is the variability of AM impedances. These devices were originally designed to have a
frequency-dependent impedance conforming to standard normal impedance,
and should be calibrated to this standard. This calibration is not entirely
simple, however, and the impedance of the articial mastoid is sensitive to
age, quality and temperature of the rubber parts. The error due to variability in AM impedance results in a dierence in audiometric zero, and should
be considered together with that of intersubject impedance variability.
From gures 11(a), 11(b), 12(a) and 12(b), it can be seen that the points
where the STD's of the force, acceleration and power become very small are
quite well dened, meaning that at these frequencies, the particular output
quantity (force, acceleration or power) is independent of the load's variability
(within the range of loads studied). In the force plot, this point lies at
1148 Hz and in the acceleration plot at 537 and 3162 Hz . From gure 10 it
can be seen that the STD of the power (measured in dB Power) behaves as
the product of the force and acceleration variabilities - having all the same
maximums, but having minimums where force and acceleration STD curves
cross each other. The frequencies where power has minimal variability are
790 and 3.9k Hz.
34
6 ANALYSIS AND DISCUSSION
70
B71 Internal Impedance
Skin Impedance
Magnitude in dB (Ns/mV)
60
50
40
30
20
10
0
125
250
500
1k
2k
4k
8k
Frequency [Hz]
Figure 18: The internal (output) impedance Zout of the B71 together with
the skin impedances ZS of the 30 subjects. Magnitude is expressed in dB
relative to 1 N s/m per Volt input.
Zg
+
Ug
+
-
Fout
-
vout
ZL
Figure 19: A representation of the system as a Thévenin equivalent of the
B71 and the load ZL
This behavior is best understood by considering the system's Thévenin
equivalent as in gure 19, and the relation between the internal impedance
6 ANALYSIS AND DISCUSSION
35
of the B71 (found by measuring the impedance at the output port with the
voltage source short-circuited) and the skin impedance as in gure 18. When
the load impedance (in this case the skin impedance ZS )is much greater
than the internal output impedance of the transducer, the B71's behavior
will approach that of an ideal voltage generator - i.e. the impedance of the
load will determine the voltage (force) across it regardless of the internal
impedance. When the internal impedance is much greater than the load
impedance (Zg ≫ ZL ) , the B71 will approach an ideal current generator in
it's behavior, providing a constant current (velocity) at the load. In gure
18, the points where the internal impedance Zg has sharp peaks due to series
and parallel resonances, it diers maximally (between 25 and 30 dB) from the
median skin impedance. These resonant peaks correspond with the points
of minimal standard deviation in gures 11(a) and 12(a). The second series
resonance at approximately 4 kHz does not coincide with such a point, as
Zg and ZL are of approximately the same magnitude at this point.
These points of negligible variability in force and acceleration are of potential value in the calibration stage of audiometery, particularly the 1148 Hz
frequency in the force. If the internal impedance of a BC transducer in the
lab is known, the calibration of the transducer/audiometer with an articial
mastoid to audiometric zero will be most reliable at this frequency. The sensitivity of the measured force to variations from standard in AM impedance
will be minimized, providing the most accurate measure of the transducer's
output condition. This point would also be the most reliable at which to
take threshold measurements. From gure 11, it is apparent that the STD
is small only at a very well-dened point, and the closest audiometry test
frequency 1000 Hz has a greater intersubject variability in the force, though
smaller than the average.
It is of interest to consider acceleration - having two such points of independence of load impedance - as the reference for audiometry. Both the mean
and standard test frequencies standard deviations of intersubject variability
are lesser for the acceleration than for the force (though not substantially), an
argument for the use of RETAL's (Reference Equivalent Threshold Acceleration Levels) instead of RETFL's. These quantities are both valid measures
of the level of stimulation from the transducer, but some arguments can be
made for the choice of force over acceleration. It is pointed out by Håkansson
et al. (1985) that the acceleration is relatively sensitive to the condition of
the skin and the contact area, due to it's dependence on the values of Cs
and Rs (see gure 6). This depence is conrmed by observing gure 17(a),
which shows that the acceleration level is substantially lower under the skin
than at the skin, whereas the force is less dependent on skin condition.
The power is also interesting to consider as a reference. It is poorly understransferedtood which factors contribute most to hearing, and one could
argue that since the power is most closely related to the total energy transfered to the skull, it could also be the best measure of what nally leads to
6 ANALYSIS AND DISCUSSION
36
stimulation of the hair cells in the cochlea. The power is represented here as
the apparent power - the vector product of the real power which is dissipated
as friction, and the reactive power which results in elastic movement and averages zero. Whether the best measure of transferred energy is reactive,
apparent, or real power is a discussion that may not be done justice here, as
it requires a better understanding of the mechanical transfer dynamics from
the surface of the skull to the cochlea.
The "golden" frequencies, where the state variables reach their minima in
variability vary depending on what quantity is of interest, but hold interest
with regards to interpretation of results that depend on these outputs as the
most reliable frequencies to observer when load impedance is unknown and
hence causes uncertainty. The region 500 − 1200 Hz has a high concentration
of these frequencies, as can be seen in gure 10.+
6.2.2
Bias Error
The dierence between the output state variables due to the dierence in
impedance between ZAM and ZS is considerable at some frequencies and zero
at others, as mentioned in section 5.2.1. Here we will discuss what relevance
and meaning this dierence has. As there are many uncertainties regarding
threshold determination, the least of which being whether or not output
force is a valid measure of hearing, a few assumptions and simplications are
rst proposed:
• We will assume that force on the skin is a valid measure of hearing.
This is fundamental in audiometry as the measure of hearing levels is
closely related to output force levels.
• We will assume that the average otologically normal and normal hear-
ing person is the average of a large number of subjects and that their
skin impedances ZS average out to the mean or median ZS shown in
this work (mean and median are very similar in this case).
• We will also assume that the mean or median skin impedance ZS M
gives rise to the mean or median output force in gures 11(a) - 13(b)
when used as the load. This has been veried in MATLAB as a reasonable assumption.
• Finally, we will assume that every articial mastoid has the same ZAM
and every B71 BC tranducer performs identically.
The averaged reference equivalent force RETFL is measured on an articial mastoid with mechanical point impedance ZAM . Referring to gure 20,
we can see that the signal required to produce this force (U0 ) is the one that
produces the threshold force F0M on the averaged normal-hearing subject
6 ANALYSIS AND DISCUSSION
37
(Subject M) who has median mechanical skin impedance ZSM . The dierence between F0M and RETFL is the bias dierence seen in gures 11(b) 13(b) between the dashed black lines and the solid black median line.
Figure 20: Force outputs from equivalent signal input with dierent load
impedances.
When an audiometric test is done on a subject (subject X in gure 20),
the force produced on that subject by input signal U0 may dier from the
force F0M produced on the averaged subject due to a dierence in skin
impedance. If the subject's skin impedance ZSX is maximally dierent from
median skin impedance ZSM , the forces F0X and F0M produced by input
signal U0 will dier maximally, the magnitude of which can exceed 10 dB at
some frequencies, as can be seen in gure 11(a). When the hearing threshold
for subject X is found, the dBHL will be shown in dB as
20 ∗ log10 (U0 /UT X )
(8)
where UT X is the signal strength at threshold for subject X. Since the dBHL
is based on the relation between input signal strengths where the reference
U0 is taken from subject M, the impedance and force on the AM are not
factors in the measure of dBHL. In fact, if the last assumption from above
held at all times, there would be no need to calibrate the BC transducer
using an articial mastoid. The bias between the median and AM output
forces in gure 11(b) is only a measure of the dierence between the RETFL
and the output force F0M .
The error in dBHL due to this method of threshold determination is
limited to the (up to and including) more than 10 dB mentioned due to
the dierence in force output audiometric zero when signal U0 is used on
6 ANALYSIS AND DISCUSSION
38
two subjects of diering ZS . If the last assumption above does not hold,
which is likely the case in many testing facilities, there is greater uncertainty,
due to the fact that RETFL produced on two AM's of diering mechanical
impedances will require dierent input signal strengths. Data on the actual
impedances of a number of AM's is required to quantify this uncertainty.
6.2.3
At Skull Bone
For the extended model, only one set of parameter values was used to represent the impedance characteristic of the skull bone, and everything to the
right of the skin parameters Cs and Rs can be looked at as one impedance
ZB (shown as Zskull in gure 21). Since ZB has such a large magnitude, it
would be expected that the force would not dier greatly between the skin
and the skull. In gures 17(a) and especially17(b), it is conrmed that the
force after transmission through the skin is similar to the force at the skin. It
is also apparent that the acceleration is substantially attenuated by the skin,
which makes sense when considering the magnitude of Cs and Rs compared
to that of ZB . The skin compliance and damping act as a shunt in the circuit,
shunting the velocity (and hence acceleration) to "ground". These results
are in good agreement with the work of Håkansson et al. (1985), where the
impact of the skin on energy transfer to the skull is discussed. The skin
impedance parameters are also similar to their ndings. In gure 17(b), it is
seen that the force on the skull is at some frequencies actually higher than
that of the skin, particularily in the 3 kHz region, where it is amplied by
the skin resonance. The mass of the skin ms becomes dominant in the higher
frequencies, attenuating the force.
Looking at gure 16(a), one nds that the points of constant acceleration
present at 537 and 3162 Hz are no longer present, and in fact there is only one
frequency where the variability in acceleration among the subjects becomes
very small, and it is located at approximately 1150 Hz. Figure 22 shows
that the skull impedance is substantially larger than the output impedance
of the transducer with the skin attached for the entire frequency range.
It seems that this would indicate a constant force output, yet the force
has a substantial mean intersubject standard deviation. In fact, the force
variability is only at a minimum at the same point as it was at the skin,
which coincides with the acceleration.
Figure 23 shows the standard deviation among the subjects for the acceleration at the skull bone is very similar to that of the force at the skin,
and seemingly identical to that of the force at the skull. This eect can
be explained if one again considers the Thévenin equivalent of the transducer including the skin. The mechanical output impedance would be the
Thévenin impedance ZT h which varies with the skin impedance, and the
Thévenin voltage source is equal to the voltage measured at the load when
it is removed, making an open circuit. As the load (the skull bone) has such
6 ANALYSIS AND DISCUSSION
39
Figure 21: The internal impedance and load impedance seen from the
skin/transducer interface and the skin/skull interface.
a large impedance, the voltage across the skin (the skin force from gure
11(a)) can be used. Both of these have only one point of near-zero intersubject deviation, 1150 Hz , and consequently the variability of the current
(velocity) and the force will have a minimum at this frequency, be equal to
each other, and dependent on the Thévenin factors when an identical load
(the skull bone) is used for each subject. In a model that considered variations in the skull impedances of the 30 subjects, this eect may not be as
apparent. In fact, due to this simplication, the observed results under the
skin should not be considered as reliable as those showing the behavior of
the transducer mechanical state variables at the skin surface.
6 ANALYSIS AND DISCUSSION
40
80
Skull Impedance
Output impedance (transducer plus skin)
Magnitude dB (Ns/mV)
70
60
50
40
30
20
10
0
125
250
500
1k
2k
4k
8k
Frequency [Hz]
Figure 22: The internal (output) impedance of the B71 and connected skin
together with the estimated skull impedance. Magnitude is expressed in dB
relative to 1
N s/m
per Volt input.
6 ANALYSIS AND DISCUSSION
41
7
Skin acceleration
Skull acceleration
Skin force
Skull force
Standard Deviation [dB]
6
5
4
3
2
1
0
2
10
3
10
4
10
Frequency [Hz]
Figure 23: The standard deviation of the force and acceleration at the skin
and at the skull bone.
7 Conclusions
With the apparent benets of percutaneous bone conduction in terms of
power consumption, comfort and sound quality, the use of transcutaneous
bone conduction transducers is today largely conned to audiology applications. The similarity in magnitude of transducer and load impedances when
using a BC driver such as the Radioear B71 makes the sensitivity of the output state variables to variations in load impedance greater than with a load
such as the skin-penetrated skull, which has a relatively high impedance.
Much of the motivation for this work lies in the uncertainty associated
with BC threshold determination. Quantitative and qualitative knowledge
about the extent of variability in transducer output is important for the
analysis and reduction of uncertainty when determining BC hearing thresholds. An investigation was done into the behavior of output force, acceleration and power from a lumped-parameter tranducer model when measured
skin impedances were used as the load (Measured impedances of 30 normalhearing subjects were taken from Cortes (2002)). These variables were modelled at the skin surface and also at the skull bone under the skin with a
Radioear B71 transcutaneous BC driver.
7.1
Main Points
Some important conclusions of this work include:
• The variability in measured skin impedances used as the load is rela-
tively consistent at all studied frequencies, with an intersubject standard deviation ranging from 2.08 to 2.79 dB.
• The variability in force, acceleration and apparent power at the skin
surface uctuates substantially across the frequency range (100 - 10000
Hz). All three state variable range from less than 0.15 dB STD up to
more than 3.5 dB STD, with the acceleration having a maximum of
4.91 dB standard deviation.
• The points at which the variability becomes negligibly small are very
well-dened, and their frequencies can be predicted with knowledge
of the mechanical output impedance of the transducer and approximate magnitude of skin impedances. These points may be of value in
audiology, e.g. for purposes of calibration for audiometry.
• At the skin surface, the points of negligible variability dier for force
and acceleration, with one well dened frequency for the force, and two
for the acceleration. Under the skin at the skull bone, there is only
one such frequency, common to the force and the acceleration.
7 CONCLUSIONS
43
• The bias between the output state variables when the load is an articial mastoid and when the load is the median human mastoid is
predictable and ranges from 0-3 dB Power in the power, 0-5 dB in the
acceleration, and 0-6 dB in the force.
• The importance of the articial mastoid impedance exactly matching
that of human mastoid is questionable in with regards to uncertainty
in hearing threshold determination. The impedance dierences between articial mastoids and between the subject being tested and the
average is of greater relevance.
7.2
Continuation
Doing the simulations has yielded some expected and some unexpected results, and of course has brought up questions that demand further exploration. Further work could be done investigating:
• Clinical or research uses for which the points of constant output accel-
eration and force can be used.
• The behaviour of the state variables at the skull bone using actual sub-
cutaneous skull impedances. The results at the skull bone obtained in
this thesis are based on the assumption of nonvarying subcutaneous
skull impedances. Lacking measured skull impedance data, multiparametric sweeps of model variables may give a more accurate portrayal
of the subcutaneous dynamics.
• The eect of manipulation of model parameters on any other part of
the model can be simulated with relative ease.
• An analysis of all sources of uncertainty or error in the audiometry
process, including that due to impedance variabilities. An objective
measure of the importance of each source or error could be determined
via a mathematical model
8 Acknowledgments
My thanks and gratitude go out to my supervisor Bo Håkanson, for his
patience and consideration while explaining many of these concepts to me,
for the time he has spent in meetings with me and for his positive attitude
and enthusiasm when discussing this work. Also many thanks go to my friend
Per Östli, who repeated times spent hours helping me with understanding
and implementing dierent parts of this project, and whose encouragement
has made it so much easier to keep going. Finally, thanks to my girlfriend
Sara, for her constant and unconditional support and kindness which have
helped me to keep my head up and complete these last ve years of my
education.
A Calculation of Transfer Function
The seven unknown variables i, v, v1−4 and Fout are represented in as many
equations, utilizing Ohm's law, Kircho's Voltage law and Kircho's Current
law. The laplace variable s is used in the derivation for simplicity, but is
replaced in MATLAB by jω .
KV L :
Ug = i · (Z1 ) + g · v
KV L :
g · i = v · Z2 + v1 · (sm1 )
KV L :
v1 ·sm1 = v2 ·sm2 +v3 ·(Z3 )
KV L :
[Z1 = Rg + R0 + sL0 + ωRω ] (9)
1
Z2 =
+ R1 (10)
sC1
1
Z3 =
+ R2 (11)
sC2
(12)
v3 · Z3 = v4 · (sm3 + ZL )
KCL :
v = v1 + v2
(13)
KCL :
v2 = v3 + v4
(14)
Fout = v4 · ZL
(15)
Ohm :
Combing (13) and (14) gives:
(16)
v = v1 + v3 + v4
(9) and (10) and (16) give:
g·
Ug − g(v1 + v3 + v4 )
= (v1 + v3 + v4 ) · Z2 + v1 · sm1
Z1
(17)
Rearranging (17) and substitution with Z4 gives:
v1 =
gUg
Z1
− v3 Z4 − v4 Z4
Z4 + sm1
g2
+ Z2
Z4 =
Z1
(18)
Using (14) and (18) in (11) and substitution with Z5 , then rearranging gives:
Z4 · sm1
v3 ·
+ sm2 + Z3
Z5
gUg · sm1
Z4 · sm1
− v4 ·
+ sm2
=
Z1 · Z5
Z5
(19)
[Z5 = Z4 + sm1 ]
Substitution with Z6 and rearranging:
gUg · sm1
Z6
v3 =
−v4 ·
Z1 · Z5 (Z6 + Z3 )
Z6 + Z3
Z4 · sm1
Z6 =
+ sm2
Z5
(20)
A CALCULATION OF TRANSFER FUNCTION
46
Using (20) in (12) yeilds:
gUg · sm1 Z3
v4 =
·Z3
+
sm
+
Z
Z1 · Z5 (Z6 + Z3 ) ZZ66+Z
3
L
3
Substitution with
Z7
Z1 · Z5 (Z6 + Z3 )
Z7 =
g · sm1
and using (15), then dividing both sides by
(21)
Ug
gives
the transfer function:
Z3 · ZL
Fout
h
i
=
·Z3
Ug
+
sm
+
Z
Z7 · ZZ66+Z
3
L
3
(22)
B MODEL PARAMETER VALUES
47
B Model Parameter Values
The lumped parameter values used in the models seen in gures 5 and 6 are
given here. Units are not shown.
Component
Ug
R0
L0
Rω
g
m1
C1
R1
m2
C2
R2
m3
Value
1
3.4
.86e-3
L0 /tan(64.6/180 ∗ pi)
3.3
16.33e-3
4.055e-6
1
2.56e-3
1.3e-6
2
3.5e-3
Table 4: Values of lumped parameter elements used in model seen in gure
5.
Component
CS (mean estimated)
mS (mean estimated)
RS (mean estimated)
Ct3
Rt3
Mt3
Rt2
Mt2
Ct1
Rt1
Ct0 (not used)
Value
4.2e − 6
7.6e − 4
14.0
220e − 9
3800
2.8
650
.09
100e − 9
320
110e − 9
Table 5: Values of median estimated skin parameters, also lumped parameter
elements used in model seen in gure 6. All values with the subscript t in
their notation are taken from Håkansson et al. (1986).
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Recommended Procedure Pure tone air and bone conduc-
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